Questions from Calculus


Q: The tangent line to the graph of y = h(x

The tangent line to the graph of y = h(x) at the point (−1, 4) passes through the point (3, 6). Find h(−1) and h′(−1).

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Q: The limit represents f′(c) for a function f and

The limit represents f′(c) for a function f and a number c. Find f and c.

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Q: The limit represents f′(c) for a function f and

The limit represents f′(c) for a function f and a number c. Find f and c.

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Q: The limit represents f′(c) for a function f and

The limit represents f′(c) for a function f and a number c. Find f and c.

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Q: The limit represents f′(c) for a function f and

The limit represents f′(c) for a function f and a number c. Find f and c.

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Q: Identify a function f that has the given characteristics. Then sketch

Identify a function f that has the given characteristics. Then sketch the function. f(0) = 2; f′(x) = −3 for −∞ < x < ∞

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Q: Identify a function f that has the given characteristics. Then sketch

Identify a function f that has the given characteristics. Then sketch the function. f(0) = 4; f′(0) = 0; f′(x) < 0 for x < 0; f′(x) > 0 for x > 0

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Q: Find equations of the two tangent lines to the graph of f

Find equations of the two tangent lines to the graph of f that pass through the indicated point. f(x) = 4x − x2

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Q: Find equations of the two tangent lines to the graph of f

Find equations of the two tangent lines to the graph of f that pass through the indicated point. f(x) = x2

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Q: Use a graphing utility to graph each function and its tangent lines

Use a graphing utility to graph each function and its tangent lines at x = −1, x = 0, and x = 1. Based on the results, determine whether the slopes of tangent lines to the graph of a function at diffe...

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